# PID or proportional-integral-derivative controller (PID controller)

As in any form of controller mechanism The PID or proportional-integral-derivative controller (PID controller) is a device that is used in a control system. The PID manages, gives an order to, facilitates, and controls the way other devices or systems operates. The difference in the design of a PID is that it does this by using mathematical calculations or algorithms that is determined by three specific parameters which are namely its proportional value, integral value, and derivative value. Calculations in the proportional value determine what the reaction to an existing error is. The integral value is understood by knowing what is the reaction based on the sum total of the recent errors. While the derivative value can determine what is the reaction by knowing the rate of change of an error. The sum of these three parameters is then taken and used to apply adjustments to the process by using a specific element for control which can be a valve or a power supply of what is being used as a heating element.

Tuning occurs when the three parameters are synchronized with each other using the algorithm of the PID controller. The controller is the mechanism that regulates and controls the action based on the specific needs or requirements of the process. The control system works as a sort of checking mechanism for possible errors, or in other words it is both the measure of the degree by which the controller exceeds the setpoint and also the level by which the system oscillates.

The PID design is a loop system. Loop systems are systems wherein different factors are regulated and are combined to achieve a designed or targeted effect. This is comparable to what we do when we adjust the water temperature between the hot and cold extremes to achieve our desired water temperature. To achieve the desired temperature we use our sense of touch to feel the temperature and base on this adjust the valves that controls the flow of the hot and cold water until we achieve equilibrium or the desired temperature setting.

In a control system a similar design occurs. Our sense of touch which is responsible for us feeling the temperature of the water is replaced by the sensors in a PID system which replaces the hand as the mechanism that measures the water temperature. This measurement is called the measurement of the process variable or PV. The temperature that we want to achieve or is desirable for the user of the shower is what is called the setpoint or the fixed point that we want to reach. Now the movement in the water valves corresponding to the hot and cold output of the faucet is now what we call as the manipulated variable or MV. The MV are factors that we could change or add to so as to change the PV and reach our setpoint or desired situation. Now in order to understand if the water is too hot or too cold one must get the difference between the

existing temperature and what is the desired one. This difference is what is called as an error. The error represents or gives a quantitative value that determines whether to adjust the MV or not.

After getting the measurements for the PV, and then determining the error, the controller will then make the decision of whether to change the values of the MV or not and how much change is necessary. For example if the existing PV is still a bit colder than the desired objective or setpoint then the controller will turn the valves corresponding to the flow of hot water a bit so as to slightly warm up the temperature of the water and bring it nearer to the setpoint. This balancing out of the manipulated variables is an example of control. Now the way the controller turns the valves determine the control that is taking place. If he turns the hot water valve slowly in the case that only a slight change in temperature is needed or if he turns it quickly in the case that how water is quickly needed to balance out the temperature, the controller is enforcing a form of proportional control. It is proportional control because the adjustments are given in proportion to the other variable. The other form of control is integral control. Integral control is when to achieve equilibrium a controller needs to turn the valves quickly to speed up the process or turn it up more in more as time passes.

In the course of implementing both proportional and integral control there is a chance that the water temperature will not remain stable and will oscillate between hot and cold temperatures because the controller either exceeds the amount of hot water or because of the frequent adjustments the controller may overshoot the desired standard or setpoint.

To compensate for the oscillation the controller may moderate the adjustments done. This is called as the derivative control method. A controller might overreached the value that is indicated by the setpoint by making to large adjustments to the MV when the indicated error is too low. When the controller continues to implement changes that are too large and has repeatedly overreached the target setpoint the system will oscillate. The system becomes unstable when the oscillations increase, but when it decreases the system becomes stable. Now to ensure the stability of the system the correct measurements and inputs should be made. The process of selecting what is the correct input or gain that should be made to ensure the effectivity of the control mechanism is called tuning the controller.

PID controllers can be tuned using different models. Generally PID controllers are tuned by providing it with the data or input based on the difference between the PV and the setpoint. In the PID this difference and the adjustments made are on the three different parameters which are the proportional, integral, and derivative term. PID is a control system that makes use of the three types of control so the difference between the PV and the setpoint is on these three variables. This is already mentioned in the explanation above regarding the different methods of implementing control.

Inputting the proportional, relative, and derivative data to adjust its values can be done in different ways. The first is by developing some sort of process model. This means making a clear model on how the whole system operates and is controlled. For our example of controlling the water temperature of the shower means making a model that would show the flow of water and how the MV influences it and what are the adjustments to be made, and what is the error occurring. Based on the model the proportional, integral, and derivative aspect should be indentified based on the parameters indicated in the working model. This manual process of tuning can be inefficient and unreliable and is only advisable is the system cannot be shut off or taken offline. If it can be shut off the more effective method for tuning is by changing the MV through a step up of input which will then be measured overtime to know the effects or response to the changed parameters of control.

The computation or formula used in the manual tuning method is first to give the integral (Ki) and derivative (Kd ) gain a value of zero. Then the proportional gain (Kp) is increased until there is an oscillation in the output. The Kp is value is then set to half to initiate what is called as a “quarter amplitude decay” reponse. The Ki is then increased until any difference is corrected. It should be noted that too much Ki will make the system instable.

After this process the Kd is then increased if necessary until the loop achieves a state wherin it is quick to reach its needed load disturbance. Again it should be noted that too much Kd can cause an overreaction or response and therefore would overshoot the setpoint. Fast tuning of PID loops can oftentimes caused a slight overshoot and would mean reaching the setpoint more quickly, while this by itself is not negative it should be pointed out that some systems cannot adapt or accept an overshoot. In cases where this happens the Kp should then be set lesser than half of that Kp setting that causes a lesser oscillation. Another method used for tuning is called tuning is the Ziegler-Nichols method. In this method the Ki and Kd are also set to zero. The proportional parameter (P) is then increased in order to achieve a critical gain or Kp which during this point the loop will start its oscillation. Kp and the period of oscillation is then used to show the value for the gains.

Since the two methods would often rely on the capability of the tuner most industrial facilities have resorted to using computer software for tuning. The calculation are now done by a computer and inputted to the system doing away with manual methods of computation. Computer software tunes PID loops by gathering the needed data by which changes are referenced or some software programs are used to gather data, construct models of the process, and also recommend means for optimal tuning.

### References

(n.d.). Control Systems And Control Systems Engineering With Classical and Modern Techniques And Advanced Concepts. (2006) Wikibooks, collection of open-content textbooks. Accessed on March 15, 2010 from the World Wide Web: http://en.wikibooks.org/w/index.php?title=Control_Systems/Print_version&printable=yes

(n.d.) PID Tutorial. On-Line document accessed on March 15, 2010 from the World Wide Web: http://www.engin.umich.edu/group/ctm/PID/PID.html

Wescott T. (2000) PID Without the PHD. On-line article accessed on March 15, 2010 from the World Wide Web: http://www.embedded.com/2000/0010/0010feat3.htm

Barr M. (2002). Introduction to Closed-Loop Control. On-line article accessed on March 15, 2010 from the World Wide Web: http://www.embedded.com/story/OEG20020726S0044

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